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Assignment 1...

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THE UNIVERSITY OF ADELAIDE AEROSPACE PROPULSION MECH ENG 4106/7053 Assignment 1 Instructions: 

Assignment is due by 5pm Friday 2nd April 2021.

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Assignments are to be submitted online on MyUni.

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This assignment is to be done individually. (i.e., no collaboration). By submitting your assignment you are agreeing to the following: I declare that all material in this assessment is my own work except where there is clear acknowledgement and reference to the work of others. I have read the University Policy Statement on Plagiarism, Collusion and Related Forms of Cheating. I give permission for my assessment work to be reproduced and submitted to other academic staff for the purposes of assessment and to be copied, submitted and retained in a form suitable for electronic checking of plagiarism.

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All relevant workings must be shown. Marks may be deducted for work that is poorly presented. Any problems that require a derivation or equation formulation will include marks for how clearly you’ve set out and explained your derivations.

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Each problem should be started on a new page and be neatly set out and clearly explained.

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For problems with MATLAB coding, you must attach your MATLAB code to your solutions as well as your resultant graphs. You must type your student ID number in both the first line of your Matlab code and the title of your graphs. Failure to adhere to these instructions may result in zero marks awarded for the entire problem. All MATLAB codes/graphs must be accompanied by clear written explanations of your workings.

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Late assignments will be penalised at 10% per day late. Late assignments will not be accepted more than one week after the due date.

Q1. Consider a turbojet engine with inlet cross-sectional area of A1 = 0.4 m2 being tested under static conditions at sea level (assume standard day conditions). (a) [7 marks] Formulate an expression (in its simplest form) for the mass flow rate, 𝑚󰇗, in terms of known (or easily calculated) parameters: (ambient pressure, 𝑃 , ambient temperature, 𝑇 , inlet area 𝐴 , ratio of specific heats, 𝛾, and specific gas constant, 𝑅 ), and the flow Mach number at the inlet (𝑀 ). Plot 𝑀 as a function of mass flow rate for a Mach number range of 0 < 𝑀 < 1. (b) [1 mark] If the mass flow rate of air entering the engine is measured to be 80.0 kg/s, what is the inlet Mach number, 𝑀 ? (c) [2 marks] Determine the additive drag of the inlet for 80.0 kg/s mass flow rate. Q2. The loss in thrust due to the inlet is defined as 𝜙 = 𝐷 /𝐹. For subsonic conditions, the additive drag 𝐷 is a conservative estimate of 𝐷 . (a) [6 marks] By considering Mattingly’s formulation of additive drag: 𝐷 = 𝑃 𝐴 (1 + 𝛾𝑀 ) − 𝑃 𝐴 𝛾𝑀 − 𝑃 𝐴 along with isentropic flow relations, show via a clearly set-out and explained derivation, that for subsonic conditions, 𝜙 can be written/estimated as: 𝜙 =

𝐷 (𝑀 /𝑀 )𝑇 /𝑇 (1 + 𝛾𝑀 ) − (𝐴 /𝐴 + 𝛾𝑀 ) = (𝐹/𝑚󰇗 )(𝛾𝑀 /𝑎 ) 𝐹

(b) [6 marks] Calculate and plot the variation of 𝜙 with flight Mach number 𝑀 from 0.20 to 0.90 for inlet Mach numbers 𝑀 of 0.60 and 0.80 with (𝐹/𝑚󰇗 )(𝛾𝑀 /𝑎 ) = 4.5. Explain the shapes/trends of the resulting graphs. Q3. [8 marks] A turbofan engine with separate exhaust streams and a bypass ratio of 5.0 is designed to operate at Mach 0.80 at an altitude of 8.0 km (where ambient temperature is 236 K). The core of the engine produces one quarter of the total thrust of the engine. The speed of the gas leaving the core is twice the flight speed of the aircraft. Determine the speed with which the gas exits the bypass nozzle. Assume the nozzles expand both exhaust streams to ambient pressure and that the mass flow rate of fuel may be neglected. Assume also that the ratio of specific heats is 𝛾 = 1.4 and the gas constant is R = 287 J/kg.K. Q4. [5 marks] Determine the optimum compressor pressure ratio and specific thrust of an ideal turbojet engine giving the maximum specific thrust at the following conditions: flight Mach number of 2.5, static freestream temperature of 220 K, total temperature at the burner exit of 1600 K, fuel heating value of hPR = 42800 kJ/kg, constant pressure specific heat of CP = 1004 J/(kg.K), and specific heat ratio of 𝛾 = 1.4. End of assignment...